[tromp]

> The task is to place four black queens and one black bishop on the chessboard so that there is no square not under their attack. In other words, after arranging the five black pieces, it must be impossible to place the white king anywhere without it being in checkmate.

That last word should be "check". not "checkmate". A king next to an unprotected queen will be in check but not checkmate as it can capture the queen.

[bryanrasmussen]

well there are all sorts of irregularities in the stated puzzle, since you cannot move into check or checkmate it follows that you should not be able to place it on the board and have it be in those conditions.

However let us suppose that you can place it on the board and have it be in either check or checkmate.

If it has been placed on the board and it is in check, since it cannot move into check it follows that it is the king's move. If it can move out of check by taking a piece or another way of moving it is not in checkmate, this seems a pretty weird trick then, because it is not so interesting that you can place the king on the board and it will be in check and it is the king's move to get out of check.

If it can get out of check by taking an unprotected queen then it is again not very interesting, and why would I not just put the king on one of those positions and take the queen from the first.

If I cannot put it on the board without it being in checkmate, it must mean that the placing it on the board is itself the move, and you cannot move into checkmate, but if placing it on the board is the move then it follows you can take a queen with that move if you can place the king anywhere on the board.

The phrasing of the puzzle is inadequate, it seems.

[Someone]

> If it can get out of check by taking an unprotected queen then it is again not very interesting

I don’t see why that would be uninteresting. Before analyzing this, it isn’t clear that there is no way to place four black queens and a black bishop on the board in such a way that they attack all blank squares _and_ defend each other against capture.

If that were the case, the puzzle where you have to find a setup where you cannot place a king on the board without it being in check is easier than the one where you have to find a setup where you cannot place a king on the board without it being in checkmate.

Also, if you interpret the puzzle description in the latter way (and that, I think, is the most natural way to do it), it seems the puzzle doesn’t have a solution (https://news.ycombinator.com/item?id=48129115)], so do you think this puzzle is not very interesting?

[jhncls]

Although unlikely, maybe there exists a solution where all black pieces are protected?

[yunwal]

If there is, it's not listed as the solution on the puzzle website

[nojs]

Yeah, the solution given is actually wrong as stated!

[chongli]

That assumes you can place the king on the board and move immediately. I think the puzzle assumes you can’t do that; that placing your king on the board is your move, thus ending your turn.

[billforsternz]

The wording is very unambiguous, it means something very specific in chess. In every legal chess position either White is checkmated or Black is checkmated or (by far the most common except in film and TV!) neither side is checkmated. So the wording is crystal clear, you should be able to freely place the White king on any of the unoccupied 59 squares and the position will be one of those in which White is checkmated.

A real shame, this totally ruined the puzzle for me as it seemed so unlikely that all five Black pieces would be mutually protected. I should have forced myself to ignore the faulty clause and try to solve without it. The bad clause is also completely unnecessary - one of those cases where deleting text (or code!) is an improvement with no downside!

[Timwi]

I'd argue that if you remove the clause you still have the same issue. The problem statement says, “so that there is no square not under their attack”, which in my reading includes the squares occupied by the pieces, and a piece cannot attack itself.

[wavemode]

There's no legal way to reach a chess position where a king is in check or checkmate and it's not the king's turn to move.

[Scarblac]

You can only be in check or checkmate when it's your turn though.